logistic(loc=0.0, scale=1.0, size=None)¶
Draw samples from a logistic distribution.
Samples are drawn from a logistic distribution with specified parameters, loc (location or mean, also median), and scale (>0).
loc : float or array_like of floats, optional
Parameter of the distribution. Default is 0.
scale : float or array_like of floats, optional
Parameter of the distribution. Should be greater than zero. Default is 1.
size : int or tuple of ints, optional
Output shape. If the given shape is, e.g.,
(m, n, k), then
m * n * ksamples are drawn. If size is
None(default), a single value is returned if
scaleare both scalars. Otherwise,
np.broadcast(loc, scale).sizesamples are drawn.
out : ndarray or scalar
Drawn samples from the parameterized logistic distribution.
- probability density function, distribution or cumulative density function, etc.
The probability density for the Logistic distribution is
where = location and = scale.
The Logistic distribution is used in Extreme Value problems where it can act as a mixture of Gumbel distributions, in Epidemiology, and by the World Chess Federation (FIDE) where it is used in the Elo ranking system, assuming the performance of each player is a logistically distributed random variable.
[R170] Reiss, R.-D. and Thomas M. (2001), “Statistical Analysis of Extreme Values, from Insurance, Finance, Hydrology and Other Fields,” Birkhauser Verlag, Basel, pp 132-133. [R171] Weisstein, Eric W. “Logistic Distribution.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/LogisticDistribution.html [R172] Wikipedia, “Logistic-distribution”, http://en.wikipedia.org/wiki/Logistic_distribution
Draw samples from the distribution:
>>> loc, scale = 10, 1 >>> s = np.random.logistic(loc, scale, 10000) >>> count, bins, ignored = plt.hist(s, bins=50)
# plot against distribution
>>> def logist(x, loc, scale): ... return exp((loc-x)/scale)/(scale*(1+exp((loc-x)/scale))**2) >>> plt.plot(bins, logist(bins, loc, scale)*count.max()/\ ... logist(bins, loc, scale).max()) >>> plt.show()